MEAN ANOMALY

In the study of orbital dynamics the 'mean anomaly' is an angle, specific to the orbiting body ''p'', which is a multiple of 2π radians at and only at periapsis. It measures the fraction of the orbit that the body has moved through since the last passage at periapsis ''z'' and is a linear function of time. In the diagram below, it is M (the angle ''zcy'').

The point ''y'' is defined such that the circular sector area ''z-c-y'' is equal to the elliptic sector area ''z-s-p'', scaled up by the ratio of the major to minor axes of the ellipse. Or, in other words, the circular sector area ''z-c-y'' is equal to the area ''x-s-z''.

Contents

Calculation

See also

Calculation

In astrodynamics 'mean anomaly' $M,!$ can be calculated as follows:
:$M\; -\; M\_0=n(t-t\_0),!$
where:

★ $M\_0,!$ is the mean anomaly at time $t\_0,!$,

★ $t\_0,!$ is the start time,

★ $t,!$ is the time of interest, and

★ $n,!$ is the mean motion.
Alternatively:
:$M=E\; -\; e\; cdot\; sin\; E,!$
where:

★ $E,!$ is orbit's eccentric anomaly,

★ $e,!$ is orbit's eccentricity.

See also

★ Kepler's laws of planetary motion

★ Eccentric anomaly

★ True anomaly